I think if you can demonstrate a need for AVI or MOV support in the Build ports, you may be able to convince someone to add support for them. That would mean making an extensive mod with decent videos etc. Possibly making a high quality version of the intro (or end game) videos for Duke or SW.

There is a program called anim2pcx that will convert ANMs to PCXs and back. Get it from RTCM.

For AVI, you would have to extract the frames, downsize them to 320x200, palettize them (not necessarily the Duke/SW palettes), convert them to PCX, form an ANM, extract the sound, and replace the default sounds with them.

I have no experience whatsoever with C(++), however I successfully managed to get enough information out of the PlayWnd example in the DX SDK to do it in Visual Basic 6.
That example project seems to have been removed out of current SDK versions. But if DirectShow is decent for you, I'll try to find it in my backups.
If your port aims to be multiplatform, DShow would be a no-go of course.

Swp does not aim to be multiplatform unless it really takes off.
Also I dont know the first thing about Basic as I'm an Assembler programmer who learned C++ through necessity at the advent of Windows 2k/Xp